# How do you differentiate #y=xcosy^2-xy#?

We can differentiate each component and then put it together

The next one is a chain differentiation and differentiation of a product

Putting it together

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To differentiate ( y = x \cos(y^2) - xy ), you would use the product rule and chain rule. The derivative with respect to ( x ) is:

[ \frac{dy}{dx} = \cos(y^2) - 2xy \sin(y^2) - y ]

This comes from differentiating ( x \cos(y^2) ) and ( -xy ) separately.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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